Bayesian Texture and Instrument Parameter Estimation From Blurred and Noisy Images Using MCMC

This letter addresses an estimation problem based on blurred and noisy observations of textured images. The goal is jointly estimating the 1) image model parameters, 2) parametric point spread function (semi-blind deconvolution) and 3) signal and noise levels. It is an intricate problem due to the data model non-linearity w.r.t. these parameters. We resort to an optimal estimation strategy based on Mean Square Error, yielding the best (non-linear) estimate, namely the Posterior Mean. It is numerically computed using a Monte Carlo Markov Chain algorithm: Gibbs loop including a Random Walk Metropolis-Hastings sampler. The novelty is double: i) addressing this fully parametric threefold problem never tackled before through an optimal strategy and ii) providing a theoretical Fisher information-based analysis to anticipate estimation accuracy and compare with numerical results.